Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 9 - Section 9.6 - Properties of Logarithms - Exercise Set: 34

Answer

$log_{9}\frac{(4x^{4}+4x)}{(x-3)}$

Work Step by Step

The quotient property of logarithms tells us that $log_{b}\frac{x}{y}=log_{b}x-log_{b}y$ (where x, y, and, b are positive real numbers and $b\ne1$). Therefore, $log_{9}(4x)-log_{9}(x-3)+log_{9}(x^{3}+1)= log_{9}\frac{(4x)}{(x-3)}+log_{9}(x^{3}+1)$. The product property of logarithms tells us that $log_{b}xy=log_{b}x+log_{b}y$ (where x, y, and, b are positive real numbers and $b\ne1$). Therefore, $ log_{9}\frac{(4x)}{(x-3)}+log_{9}(x^{3}+1)= log_{9}\frac{(4x)}{(x-3)}\times(x^{3}+1)= log_{9}\frac{(4x(x^{3}+1))}{(x-3)}=log_{9}\frac{(4x^{4}+4x)}{(x-3)}$.
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